Help understanding Problem

In this Problem: https://brilliant.org/practice/integration-u-substitution-given-u/?p=4 (copy paste to get to hyperlink)

It says that the answer is 3/16 ln2. My question is how did it arrive to that answer? I understand everything up until -3/8 ln 1/(root 2) became 3/16 ln2. Thank you for helping me understand this. I am slightly confused, and I would like to fix that.

Easy Math Editor

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Comments

Recall that with logs,

$a \, ln (b) = ln(b^a)$

So then:

$-\frac{3}{8} ln \Big(\frac{1}{\sqrt{2}} \Big) \\ = \frac{3}{8} ln \Big(\sqrt{2} \Big) \\ =\frac{3}{16} \, 2 \, ln \Big(\sqrt{2} \Big) \\ = \frac{3}{16} ln \Big(2 \Big)$

Steven Chase - 1 year, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$